1. Field of the Invention
The present application relates generally to methods of estimating the optical nonlinearity profile of a material.
2. Description of the Related Art
In thermal poling of silica, a silica wafer is heated (e.g., to approximately 270 degrees Celsius) while an external voltage (e.g., approximately 5 kilovolts) is applied to the wafer. This process induces a second-order nonlinear region under the anode electrode, and this nonlinear region does not decay upon cooling the wafer to room temperature and removing the applied voltage. The depth profile of this induced nonlinear region is often non-uniform and can have a variety of functional forms. The depth profile is a key parameter for understanding the theory of poling, improving the strength and/or width of the induced nonlinear region, and for the design of poled electro-optics devices.
The Maker fringe technique, as described by P. D. Maker et al. in “Effects of dispersion and focusing on the production of optical harmonics,” Physical Review Letters, Vol. 8, pp. 21-22 (1962), is a method for obtaining information regarding the nonlinearity profile of a material. It involves focusing a laser beam onto the material (e.g., an optically nonlinear wafer) and measuring the generated second-harmonic (SH) power as a function of the laser incidence angle (θ). The dependence of the SH power on θ is known as the Maker fringe (MF) curve, and is proportional to the square of the Fourier transform magnitude of the nonlinearity profile d(z). For thin films under study, z is in the direction perpendicular to the thin film. Consequently, in principle, d(z) is retrievable by inverting this Fourier transform. However, d(z) cannot be retrieved without the knowledge of the phase of this Fourier transform, which is not provided by the measurement of the MF curve. In the past, this limitation has been mitigated by assuming that d(z) has a given shape (e.g., Gaussian) and using a fitting process, but this approach fails to provide the actual nonlinearity profile d(z).
Recently, this problem was solved by introducing a new family of inverse Fourier Transform (IFT) techniques that involve measuring the MF curves of sandwich structures formed by mating two optically nonlinear samples. As a result of interference between the samples, these MF curves contain the phase of the Fourier transform of the nonlinearity profiles, and the profiles can be recovered uniquely. Examples of these IFT techniques are described in U.S. patent application Ser. No. 10/357,275, filed Jan. 31, 2003, U.S. patent application Ser. No. 10/378,591, filed Mar. 3, 2003, and U.S. patent application Ser. No. 10/645,331, filed Aug. 21, 2003. These IFT techniques are further described by A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Inverse Fourier Transform technique to determine second-order optical nonlinearity spatial profiles,” Applied Physics Letters, Vol. 82, pp. 1362-1364 (2003) [Ozcan I]; A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Erratum: Inverse Fourier Transform technique to determine second-order optical nonlinearity spatial profiles,” Applied Physics Letters, Vol. 83, p. 1679 (2003) [Ozcan II]; A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Improved technique to determine second-order optical nonlinearity profiles using two different samples,” Applied Physics Letters, Vol. 84, No. 5, pp. 681-683 (Feb. 2, 2004) [Ozcan III]; A. Ozcan, M. J. F. Digonnet, and G. S. Kino, “Simplified inverse Fourier transform technique to measure optical nonlinearity profiles using a reference sample,” Electronics Letters, Vol. 40, No. 9, pp. 551-552 (Apr. 29, 2004) [Ozcan IV].